Zero Modes of Rotationally Symmetric Generalized Vortices and Vortex Scattering

Zero modes of rotationally symmetric vortices in a hierarchy of generalized Abelian Higgs models are studied. Under the finite-energy and the smoothness condition, it is shown, that in all models, $n$ self-dual vortices superimposed at the origin have $2n$ modes. The relevance of these modes for vortex scattering is discussed, first in the context of the slow-motion approximation. Then a corresponding Cauchy problem for an all head-on collision of $n$ vortices is formulated. It is shown that the solution of this Cauchy problem has a $\frac{\pi}{n}$ symmetry.Comment: 12 pages. late

The Optical Soliton Contents of some Special Input Pulses

The optical soliton contents of some special input pulses and their Galilei transforms will be determined by solving the linear eigenvalue problem associated with the non-linear Schrödinger equation. The special cases discussed are the initial envelope function of width a and height β, the initial envelope function —iβ*exp(—α|x|) and the super-Gaussian initial pulse. Throughout, we compare our problem to the Korteweg-de Vries problem where a good understanding can be gained through Sturm-Liouville theory

Statics and Dynamics of Classical Yang-Mills-Higgs Systems: Some Recent Developments

Some classical Yang-Mills-Higgs solutions, all characterized by an underlying nontrivial topology, are studied. First, the explicit construction of magnetic n-pole solutions is briefly reviewed. Second, theories which allow for noncontractible loops and static saddle points which result from this type of nontrivial topology are exhibited. We then turn to time-dependent solutions. Here, we first state the underlying ideas for the description of the scattering of slowly-moving monopoles. Finally, Segal’s theorem is discussed and the existence proofs for time-dependent vortices and monopoles, which apply to the equations of motion without any approximation, are outlined

Time Dependent Vortices and Monopoles

We discuss the relevance of global existence proofs. The underlying mathematical theory is outlined, and it is shown how additional problems in the case of vortices and monopoles can be overcome. Ways of building on the existence proofs are indicated

Instanton Induced Tunneling Amplitude at Excited States with the LSZ Method

Quantum tunneling between degenerate ground states through the central barrier of a potential is extended to excited states with the instanton method. This extension is achieved with the help of an LSZ reduction technique as in field theory and may be of importance in the study of macroscopic quantum phenomena in magnetic systems.Comment: 8 pages, LaTex, no figure

On the Construction of Higgs Sectors

The problem of constructing Higgs sectors, that is. finding Higgs representations and potentials that will produce a given spontaneous breakdown G → H (or hierarchy G → H → K...) is considered from a general point of view. The concepts of ordering of little groups, of little spaces and of symmetric algebras are shown to be of use, and it is also shown that in many cases a sum-of-squares potential can be very effective. A number of applications are presented and the pseudo-Goldstone problem is discussed

Disconnected Non-maximal Stability Groups and Horizontal Symmetry

We study the (2,2) representation of SU(3) and show that in this case non-maximal and disconnected stability subgroups exist. From this particular example we extract a general rule for obtaining non-maximal stability groups. The resulting principle is applied to SO(16) Grand Unified Theory. We build a model with four left-handed and four right-handed families and with W_4 (Weyl Group of SU(4)) as the discrete horizontal symmetry group

Finite-Action Solutions of Higher-Order Yang-Mills-Higgs Theory in Four Dimensions

We study (generalized) Yang-Mills-Higgs theories with higher-order terms. We present topologically nontrivial finte-action solutions in a mini-model and discuss a more relevant model later. Although the ansatz we choose is not S0(4) symmetric it leads to SO(4) invariant action densities and is compatible with the equations of motion for a wide class of models

A Study of a 90° Vortex-Vortex Scattering Process

Following Ruback, we discuss the evidence for scattering at right angle of two vortices in a head-on collision. The evidence is given in terms of the approximate solutions of the equations of motion. This makes it possible to extend the analysis to the case of a small net repulsive force between the corresponding static vortex configurations.The ordinary differential equations, which result from the ansatz for the approximate solutions, are solved by Taylor series at the origin and by asymptotic series at infinity